@Markiyan Hirnyk Please see the proof added above.

@J4James If alpha > 0 and beta > 0  then the first root found by Maple is real and the next two are imaginary. This follows from the fact that the cube root appearing in all the 3 results is the cube root of a positive number, thus real.

alpha*x+beta*x^3=f2;
r:=solve(%,x);
r[1];
op([1,1],indets(r[1],`^`(anything,1/3)));
#This is greater than or equal to
eval(%,alpha=0);
simplify(%) assuming real;
#which is >= 0.

#Of course if beta=0 and alpha > 0 there is only one solution.

If beta <0 you will observe that the situation is more complicated:

animate(complexplot,[[eval(r,{alpha=1})],f2=-10..10,thickness=3],beta=-5..5);

@J4James If alpha > 0 and beta > 0  then the first root found by Maple is real and the next two are imaginary. This follows from the fact that the cube root appearing in all the 3 results is the cube root of a positive number, thus real.

alpha*x+beta*x^3=f2;
r:=solve(%,x);
r[1];
op([1,1],indets(r[1],`^`(anything,1/3)));
#This is greater than or equal to
eval(%,alpha=0);
simplify(%) assuming real;
#which is >= 0.

#Of course if beta=0 and alpha > 0 there is only one solution.

If beta <0 you will observe that the situation is more complicated:

animate(complexplot,[[eval(r,{alpha=1})],f2=-10..10,thickness=3],beta=-5..5);

You are referring to mbogo:

http://www.mapleprimes.com/questions/139205-Graphing-And-Parameter-Sensitivity-Analysis

I don't believe Maple can help you solve that type of problem.

You are referring to mbogo:

http://www.mapleprimes.com/questions/139205-Graphing-And-Parameter-Sensitivity-Analysis

I don't believe Maple can help you solve that type of problem.

@Adri vanderMeer van der Meer I think it is a floating point issue.

Consider the output from these lines:

restart;
f:=proc(theta::numeric) print(theta); csc(theta)^2 - cot(theta)^2 end proc;
plot(f, 0..2*Pi,numpoints=5,adaptive=false,style=point ,symbolsize=20);
plottools:-getdata(%);
A:=%[-1];
A[4,1];
f(%);
seq( evalf[n](f(A[4,1])),n=10..25);

@Adri vanderMeer van der Meer I think it is a floating point issue.

Consider the output from these lines:

restart;
f:=proc(theta::numeric) print(theta); csc(theta)^2 - cot(theta)^2 end proc;
plot(f, 0..2*Pi,numpoints=5,adaptive=false,style=point ,symbolsize=20);
plottools:-getdata(%);
A:=%[-1];
A[4,1];
f(%);
seq( evalf[n](f(A[4,1])),n=10..25);

How is mean(X(t)) defined? And what about V(t)?

Since there is only one independent variable (t) you don't have a pde.

To avoid that the best is to go to

Tools/Options/Display/Input display : Choose Maple Notation

after that I would also go to

Tools/Options/Interface/Default format for new worksheets : Choose Worksheet

Finally click on the button Apply Globally

To see that these are in effect, open a new worksheet and start writing.

These options can always be changed, if you don't like them.

To avoid that the best is to go to

Tools/Options/Display/Input display : Choose Maple Notation

after that I would also go to

Tools/Options/Interface/Default format for new worksheets : Choose Worksheet

Finally click on the button Apply Globally

To see that these are in effect, open a new worksheet and start writing.

These options can always be changed, if you don't like them.

@Krischu If you use 1D input (Maple input) it is probably a good idea to define A before you introduce the values. That way you will be able to see if you typed correctly:

restart;
A := abs((-2*b/lambda^3-4*c/lambda^5)*2*a*sin(1/2*epsilon)/cos((delta[min]+epsilon)/2));
b := 24649.42;
c := -1.37*10^9;
lambda := 578;
a := 0.1e-2*10^9;
epsilon := 60*Pi*(1/180);
delta[min]:= 59.64*Pi*(1/180);
A;
evalf(A);

@Krischu If you use 1D input (Maple input) it is probably a good idea to define A before you introduce the values. That way you will be able to see if you typed correctly:

restart;
A := abs((-2*b/lambda^3-4*c/lambda^5)*2*a*sin(1/2*epsilon)/cos((delta[min]+epsilon)/2));
b := 24649.42;
c := -1.37*10^9;
lambda := 578;
a := 0.1e-2*10^9;
epsilon := 60*Pi*(1/180);
delta[min]:= 59.64*Pi*(1/180);
A;
evalf(A);

Try evalf(A);

It is easier for us to be helpful if instead of a picture you upload a worksheet via the fat green arrow in MaplePrimes.

Try evalf(A);

It is easier for us to be helpful if instead of a picture you upload a worksheet via the fat green arrow in MaplePrimes.

@Cody I have uploaded a worksheet. You should know that I don't know much about statistics, so use your own judgement!

MaplePrimes12-10-2.mw